@article {60,
	title = {Complexities of Horn Description Logics},
	journal = {ACM Trans. Comput. Log.},
	volume = {14},
	year = {2013},
	pages = {2},
	abstract = {Description Logics (DLs) have become a prominent paradigm for representing knowledge bases in a variety of application areas. Central to leveraging them for corresponding systems is the provision of a favourable balance between expressivity of the knowledge representation formalism on the one hand, and runtime performance of reasoning algorithms on the other. Due to this, Horn description logics (Horn DLs) have attracted attention since their (worst-case) data complexities are in general lower than their overall (i.e. combined) complexities, which makes them attractive for reasoning with large sets of instance data (ABoxes). However, the natural question whether Horn DLs also provide advantages for schema (TBox) reasoning has hardly been addressed so far. In this paper, we therefore provide a thorough and comprehensive analysis of the combined complexities of Horn DLs. While the combined complexity for many Horn DLs studied herein turns out to be the same as for their non-Horn counterparts, we identify subboolean DLs where Hornness simplifies reasoning. We also provide convenient normal forms for Horn DLs.},
	keywords = {computational complexity, description logics, Horn logic},
	doi = {10.1145/2422085.2422087},
	url = {http://doi.acm.org/10.1145/2422085.2422087},
	author = {Markus Kr{\"o}tzsch and Sebastian Rudolph and Pascal Hitzler}
}
@conference {124,
	title = {Recent Advances in Integrating {OWL} and Rules},
	booktitle = {Web Reasoning and Rule Systems - 6th International Conference, RR 2012, Vienna, Austria, September 10-12, 2012. Proceedings},
	volume = {7497},
	year = {2012},
	month = {09/2012},
	pages = {225-228},
	publisher = {Springer},
	organization = {Springer},
	address = {Austria, Vienna},
	abstract = {As part of the quest for a unifying logic for the Semantic Web Technology Stack, a central issue is finding suitable ways of integrating description logics based on the Web Ontology Language (OWL) with rule-based approaches based on logic programming. Such integration is difficult since naive approaches typically result in the violation of one or more desirable design principles. For example, while both OWL 2 DL and RIF Core (a dialect of the Rule Interchange Format RIF) are decidable, their naive union is not, unless carefully chosen syntactic restrictions are applied.

We report on recent advances and ongoing work by the authors in integrating OWL and rulesWe take an OWL-centric perspective, which means that we take OWL 2 DL as a starting point and pursue the question of how features of rulebased formalisms can be added without jeopardizing decidability. We also report on incorporating the closed world assumption and on reasoning algorithms. This paper essentially serves as an entry point to the original papers, to which we will refer throughout, where detailed expositions of the results can be found.},
	keywords = {description logics, OWL, Rules},
	doi = {10.1007/978-3-642-33203-6_20},
	url = {http://dx.doi.org/10.1007/978-3-642-33203-6_20},
	author = {Matthias Knorr and David Carral and Pascal Hitzler and Adila Krisnadhi and Frederick Maier and Cong Wang},
	editor = {Markus Kr{\"o}tzsch and Umberto Straccia}
}
@article {65,
	title = {Type-Elimination-Based Reasoning for the Description Logic SHIQbs using Decision Diagrams and Disjunctive Datalog},
	journal = {Logical Methods in Computer Science},
	volume = {8},
	year = {2012},
	abstract = {We propose a novel, type-elimination-based method for standard reasoning in the description logic SHIQbs extended by DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) that represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst-case optimal w.r.t. combined and data complexity.},
	keywords = {datalog, decision diagrams, description logics, type elimination},
	doi = {10.2168/LMCS-8(1:12)2012},
	url = {http://dx.doi.org/10.2168/LMCS-8(1:12)2012},
	author = {Sebastian Rudolph and Markus Kr{\"o}tzsch and Pascal Hitzler}
}
@conference {139,
	title = {A Better Uncle for {OWL}: Nominal Schemas for Integrating Rules and Ontologies},
	booktitle = {Proceedings of the 20th International Conference on World Wide Web, WWW 2011, Hyderabad, India, March 28 - April 1, 2011},
	year = {2011},
	month = {03/2011},
	pages = {645-654},
	publisher = {ACM},
	organization = {ACM},
	abstract = {We propose a description-logic style extension of OWL 2 with nominal schemas which can be used like "variable nominal classes" within axioms. This feature allows ontology languages to express arbitrary DL-safe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worst-case reasoning complexity, and we identify a novel tractable language SROELV3(\cap, x) that is versatile enough to capture the lightweight languages OWL EL and OWL RL.},
	keywords = {datalog, Description Logic, Semantic Web Rule Language, SROIQ, tractability, Web Ontology Language},
	isbn = {978-1-4503-0632-4},
	doi = {10.1145/1963405.1963496},
	url = {http://doi.acm.org/10.1145/1963405.1963496},
	author = {Markus Kr{\"o}tzsch and Frederick Maier and Adila Krisnadhi and Pascal Hitzler},
	editor = {Sadagopan Srinivasan and Krithi Ramamritham and Arun Kumar and M. P. Ravindra and Elisa Bertino and Ravi Kumar}
}
